Review

Statistics Types• Descriptive – describe the data, create a picture of the data• Mean – average of all scores• Mode – score that appears the most often• Median – score that appears in the middle when arranged in

order• Variance – average distance of scores from the mean• Standard deviation – standardized variance (or standard average

distance from the mean)

Data Set• To get all descriptive information at once• Two different ways• Open the basic data set.sav

• Analyze > frequencies• OR• Analyze > descriptive statistics

Frequency Output• First box gives you:• Mean, median, mode, variance, standard deviation

• Next set of boxes are frequency tables• List all the scores and how many of them fall into those scores

• On this output, we also asked for histograms

Descriptives output• Will only give you:• Mean, standard deviation, variance (if you ask), min and max• SE = standard error of mean or standard deviation of the

distribution of samples• Does not do median, mode• Will give you standardized scores (z-scores)

Statistics Types• Inferential statistics• Infer information about the data. • Tells you if your data is different from some known sample OR

some other data set.• Parametric versus non-parametric• Parametric – used on interval and ratio data, numbers that are

continuous in nature• Requires more assumptions

• Non-parametric – used on all data types (especially nominal, categorical)• Does not require same assumptions

Hypothesis Testing• “Surely God loves p<.06 just as much as p<.05” – Jacob Cohen• Hypothesis Tests• Null (want to reject this)

• All groups are equal, IVS and DVS unrelated, Expected=Observed, etc.

• Alternative • Groups are not equal, one mean > another mean, expected doesn’t

equal observed etc.

Hypothesis Testing• In basic statistics:• Usually you learn about cut off scores and the score has to be

greater than the cut off score to be significant• You are finding the point in which the probability of that score is

less than 5% or 1%.

Hypothesis Testing• Another way to think about this:• Instead just use exact p-values.• SPSS will give you the p-value. You want your p-values to be less

than .05 or .01.• Eliminates the need for cut off scores (sort of)• Not for z-tests• Not for post hoc tests • Not for one tailed tests

• Always uses a two-tailed test (if applicable).

Univariate Statistics• Univariate – 1+ IVs to 1 DV• Most common used• Limit you to only one DV

• Types• Z• T-tests• ANOVA**• Correlation• Regression**• Chi-Square

Univariate• Z-tests• Types:

• X-score• Z-test (single sample)

• Assumptions• Normal distributions

Z-score example• A personnel psychologist has to decide which of three

employees to place in a particular job that requires a high level of coordination. All three employees have taken tests of coordination, but each took a different test. Employee A scored 15 on a test with a mean of 10 and a standard deviation of 2; Employee B scored 350 on a test with a mean of 300 and a standard deviation of 40; and Employee C scored 108 on a test with a mean of 100 and a standard deviation of 16. (On all three tests, higher scores mean greater coordination.)

• Who’s the best?

Z-Test example• In a study to see if children from lower socio-economic status

(SES) neighborhoods have lower than average test-taking skills, a psychologist administered a standard measure of test-taking skills to a set of randomly chosen children from a low SES neighborhood and found them to have a score of 38. The average score on this measure for the population in general is 50 with a standard deviation of 10. Using the .05 level of significance, what conclusions should be drawn about whether children from low SES neighborhoods have lower test-taking ability?

T-Tests• Types:• Single sample• Dependent• Independent

• Assumptions• Normal curves• Equal Variances (homogeneity)

Single Sample Example• A school has a gifted/honors program that they claim is

significantly better than others in the country. The national average for gifted programs is a SAT score of 1250. • Use the file single sample t-test here.

Dependent T-test• In a study to test the effects of science fiction movies on people's belief in the

supernatural, seven people completed a measure of belief in the supernatural before and after watching a popular science fiction movie. Participants' scores are listed below with high scores indicating high levels of belief. Using the .01 significance level, carry out a t test for dependent means to test the experimenter's assumption that the participants would be less likely to believe in the supernatural after watching the movie.

• Belief-in-Supernatural Scores, Before and After • Watching Science Fiction Movie

• Participant Before After • A 3 3• B 5 3• C 9 6• D 6 8• E 7 8• F 5 2• G 4 1

Independent Sample• A forensic psychologist conducted a study to examine whether

being hypnotized during recall affects how well a witness can remember facts about an event. Eight participants watched a short film of a mock robbery, after which each participant was questioned about what he or she had seen. The four participants in the experimental group were questioned while they were hypnotized and gave 14, 22, 18, and 17 accurate responses. The four participants in the control group gave 20, 25, 24, and 23 accurate responses. Using the .05 significance level, do hypnotized witnesses perform differently than witnesses who are not hypnotized?

Correlation/Regression• Types• Pearson’s r• Spearman’s rho• Simple Linear Regression

• Assumptions• Normality• Homogeneity• Homoscedasticity

Correlation Example• Scores were measured for femininity and sympathy (see

correlation.sav). Is there a correlation between those two variables?

Chi-Square• Note: Chi-square is a non-parametric test.• Assumptions• Each person can only be in one category• Minimal categories

Chi-Square Example• The following table shows results of a survey conducted at a

particular high school in which students who had a small, average, or large number of friends were asked whether they planned to have children.

Multivariate Statistics• Multivariate – 1+ IVs to 1+ DVs• Types• MANOVA/MANCOVA• Profile Analysis (repeated measures)• Multiple Regression• Discriminant Analysis• Log Regression• Factor Analysis• Canonical Correlations• Frequency Analysis